Inhibitory-stabilized network (ISN) models of the cerebral cortex predict that local (recurrent) synaptic connectivity plays a vital role in shaping cortical activity. Yet it has been experimentally unclear if cortical recurrent connectivity is strong enough to make ISNs good descriptions of cortical function. Here we test several ISN predictions, including the counterintuitive (paradoxical) suppression of inhibitory firing when the inhibitory network is stimulated. We pair, in awake mice, optogenetic stimulation of all inhibitory subtypes with in vivo pharmacology to identify inhibitory cells. We observe responses consistent with an ISN in the upper layers of visual, somatosensory, and motor cortex. Stimulating parvalbumin (PV)-positive inhibitory neurons produces a population paradoxical effect only with transgenic, not viral, opsin expression. This effect is explained in a model where viral expression targets a subset of PV cells, showing inhibitory cell responses to stimulation can be highly dependent on the number of stimulated cells.